A gramophone record is revolving with an angular velocity w....

A gramophone record is revolving with an angular velocity $w$. A coin is placed at a distance $r$ from the centre of the record. The coefficient of static friction is. The coin will revolve with the record if (A) $\mathrm{r}=\mathrm{gw}^{2}$ (B) $\mathrm{r}<\left(\mathrm{w}^{2} / \mathrm{g}\right)$ (C) $r<\left(g / w^{2}\right)$ (D) $r \geq\left(g / w^{2}\right)$

A gramophone record is revolving with an angular velocity
$w$. A coin is placed at a distance $r$ from the centre of the record. The coefficient of static friction is. The coin will revolve with the record if
(A) $\mathrm{r}=\mathrm{gw}^{2}$
(B) $\mathrm{r}<\left(\mathrm{w}^{2} / \mathrm{g}\right)$
(C) $r<\left(g / w^{2}\right)$
(D) $r \geq\left(g / w^{2}\right)$

Key Concepts

Force Equilibrium in Rotational Motion

This concept involves balancing the forces acting on an object in uniform circular motion. Specifically, the maximum static friction force must be equal to or greater than the centripetal force requirement for the object to remain in its circular path. Establishing this balance is essential to determine conditions, such as the maximum radius for stable rotation.

Angular Velocity

Angular velocity quantifies the rate of rotation of an object around a central point and is measured in radians per second. It is crucial in calculations involving rotational motion because the required centripetal force is proportional to the square of the angular velocity.

Centripetal Force

This concept refers to the inward force required to keep an object moving in a circular path. It is calculated as the product of mass, the square of the angular velocity, and the radius of the circle. In problems involving rotational motion, recognizing how centripetal force sustains circular trajectories is fundamental.

Static Friction

Static friction is the force that prevents an object from sliding when it is in contact with a surface. In the context of circular motion, static friction is responsible for providing the centripetal force needed to keep the object from sliding out of its circular path. Understanding the maximum limit of static friction, determined by the friction coefficient and the normal force, is key.

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